"Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles" (for a brief historical account on this topic, see here and here on MathWorld).

Consider the triangle formed by the centers of these circles, one can draw a new set of smaller Malfatti circles in this triangle. What is the limiting point of this process?

One thing sort of discouraging is that I tried on an isosceles triangle, unfortunately did not find the limiting point matching any of the known relevant points (e.g., incenter or the first Ajima-Malfatti point).

@David, Thank you for your prompt reply! The website is extremely nice, but unfortunately, my numerical calculation (please feel free to cross-check) shows the first normalized trilinear coordinate is 1.4377 for a triangle with (a,b,c)=(6,9,13), which does not match any of the entries listed there. It's a little disappointing, but I will mark your answer as the accepted answer.
–
kiasncpJan 31 '10 at 1:06

2

Disappointing? This means you can claim credit for a new center!
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David EppsteinJan 31 '10 at 2:15